Theorems · Definition · functional analysis
AbsConvex
(𝕜 : Type u_1) → {E : Type u_2} → [SeminormedRing 𝕜] → [SMul 𝕜 E] → [AddCommMonoid E] → [PartialOrder 𝕜] → Set E → PropA set is absolutely convex if it is balanced and convex.
- Defined in
- Mathlib.Analysis.LocallyConvex.AbsConvex
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- Convexproof · cited by 551
- SeminormedRingstatement and proof · cited by 446
- Balancedproof · cited by 77
Cited by34
Results whose statement or proof uses this declaration.
- absConvexHullproof · cited by 29
- closedAbsConvexHullproof · cited by 10
- AbsConvexOpenSetsproof · cited by 8
- absConvexHull_minstatement · cited by 4
- absConvex_absConvexHullstatement · cited by 4
- AbsConvex.sInterstatement and proof · cited by 3
- AbsConvexOpenSets.coe_isOpenstatement · cited by 3
- AbsConvex.closurestatement and proof · cited by 2
- AbsConvexOpenSets.coe_zero_memstatement · cited by 2
- nhds_hasBasis_absConvexstatement and proof · cited by 2
- nhds_hasBasis_absConvex_openstatement and proof · cited by 2
- closedAbsConvexHull_minstatement and proof · cited by 1